The sets of numbers 6, 8, 10 and 5, 12, 13 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples

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The sets of numbers 6, 8, 10 and 5, 12, 13 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples

Mathematics

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Directrix

2 years ago

5, 12, 13
Show that this triple satisfies the Converse of the Pythagorean Theorem:
Pythagorean Thereom converse: If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
5^2+ 12^2 = 13^2
25 + 144 = 169
169 = 169
@Redneckk__Lifee I saved the first triple for you.

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Pythagorean Theorem is known as a^2 +b^2 = c^2, and it is only used if and only if the triangle is a right triangle. Some Pythagorean triples, smallest like 3,4,5 , have the same total at the end
To met a Pythagorean triples, they must requires:
a +b > c and a^2 + b^2 = c^2
Ex: a=3, b=4, c=5
3 +4 >7
\[3^{2} + 4^{2} = 5^{2}\]
9 +16 =25
25 =25
If a +b c and \[a ^{2} +b ^{2} \neq c ^{2}\] , then it is not a triangle
Example: 4,5,6
4 +5 >6
\[4^{2} +5^{2} \neq 6^{2}\]

anonymous

2 years ago

okay, we have 6, 8, 10 and 5, 12, 13, as you know the formula is a^2 + b^2=c^2. And now how do we know which one is a,b and c? easy, a and always smaller than c so any 2 number in the given number that smaller than the third, is a and b, the last one is c :) now let's solve it:
6, 8, 10
a^2+b^2=c^2
6^2+8^2=10^2
( 6 and 8 both smaller than 10 so it makes sense that 6 and 8 is a and b, 10 is c :) )
36 + 64 =100
100=100 (true ) this would form a right triangle :)
5, 12, 13,
5 and 12 both smaller than 13, so it makes sense that 5 and 12 is a and b, 13 is c :)
5^2 + 12^2 =13^2
25 + 144 = 169
159 = 169. ( false ) a^2+b^2 must =c^2 !!! it can't not be neither bigger or smaller :3 must be equal :3 there you go :3